文章基本信息

标题：A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
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作者：Davis-Stober, Clintin P. ; Doignon, Jean-Paul ; Suck, Reinhard 等
期刊名称：Frontiers in Psychology
电子版ISSN：1664-1078
出版年度：2015
卷号：6
页码：1767-1772
DOI：10.3389/fpsyg.2015.01767
出版社：Frontiers Media
摘要：We consider the sample covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950).
关键词：Guttman scale; Dichotomous items; Rasch model; Principal Component Analysis; Eigenvalues; eigenvectors